Ohm’s law and its derivation

MOBILITY OF THE ELECTRON AND CURRENT

Mobility of electron (ue) is defined as the drift velocity of electron per unit electric field applied.

ue= drift velocity/electric field= Vd/E

Thus                                 Vd=ueE

The  SI unit of mobility is m2s-1V-1 or ms-1N-1C

As  by the relation of the current and drift velocity (already discussed)

I=Anevd (1)

By putting value of vd in above equation we get

I=AneueE

OHM’S LAW

Statement:– Ohm’s law states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the ends of the conductor,provided physical conditions of the conductors such as temperature,mechanical strain etc. Are kept constant i.e. IαV

Or                                                   VαI or V= RI

Or                                                   V/I=R=a constant

Where R is known as resistance of the conductor . It depends upon the length ,shape and the nature of the material of the conductor. The variation between potential difference (V) and current (I) through a conductor is a straight line.

Deduction of Ohm’s Law:

As drift velocity is given by Vd=eEt/m

But                         Electric field across the conductor of length l is

E=V/l

Thus                              Vd=e V/ml

Also,                              I=Anevd

By putting value of vd in the equation of I (equation 1 of relation of the current and drift velocity),we get

I=Ane(eV/ml)=(Ane2/ml)V

Or                        V/I=ml/Ane2=R

Where R is a constant for a given conductor. It is known as the resistance of the conductor.

Thus                                  V=RI

This  is Ohm’s law.

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